I haven't heard anything about you gaining more Honor for writing an After Action Report, so I don't think that's the case. If it was, players with one point of honor (because of leaving games and other frustrating behavior) could simply write an AAR after each completed battle and keep their honor up to hide their other behavior...

At this point I don't know what happens with the report. I think the hope will be to eventually link them to your User Page or something like that, but I think it's a low priority for the team.

I had a very exciting and noteworthy battle where me and my opponent immideately started writing AARs. Sadly we could not find the correct way to acknowledge each other so the AARs were lost, ultimately.